Peer Institutes¶

Introduction¶

Within higher education, peer institutes are colleges and universities similair to your own, based on shared characteristics such as academic offerings, enrollment, admissions criteria, and financials measures. These schools are used as benchmarks to evaluate performance, set goals, and inform strategic planning.

In my experience, most institutions do not use a particularly rigorous or data-driven methodology when selecting peer institutions. Instead, peer schools are often chosen by senior leadership based on subjective perceptions. As a result, peer lists frequently include aspirational peers rather than true comparables.

Here, I present a simple, quantitative methodology for indentying peer institutes.

Data & Packages¶

First, we'll load the necessary packages and data. The dataset comes from the U.S. Department of Education’s Integrated Postsecondary Education Data System (IPEDS). The data has already been cleaned, so I won’t be covering that process here—but if you’re interested, you can check it out here.

The final dataset includes 20 variables for 507 public universities. These variables are wide-ranging and were selected to provide a holistic portrait of each institution. I won’t go into detail on each one, but they include:
Admit Rate Yield Rate
Percentage of Freshmen Receiving a Pell Grant Percentage of Freshmen Receiving Institution Grant Aid
Percentage of Freshmen who are Living On Campus Total Number of Graduate Students
Total Number of Degree Seeking Undergraduates Total Number of Non-Degree Seeking Undergraduates
Four Year Graduation Rate Six Year Graduation Rate
Percentage of Freshmen who are In-State Instructional Expenses per Undergraduates
Research Expenses per Undergraduate Endowment per Undergraduate
Percentage of Revenue coming from Tuition Discount Rate
In-State Tuition Out-of-State Tuition
Student-Faculty Ratio Retention Rate
In [1]:
## loading packages
import pandas            as pd
import numpy             as np
import matplotlib.pyplot as plt
import seaborn           as sns

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.metrics       import pairwise_distances

## loading data
df_ipeds = pd.read_csv("clean_data.csv")

Data Prep¶

First, the dataset includes several count-based variables that are highly skewed, so we’ll apply a log transformation to those. Then, we’ll scale the data using Z-score normalization.

In [2]:
## log transforming some variables
df_scaled = (df_ipeds
             .assign(ENROLL_GRAD_ALL     = np.log(df_ipeds["ENROLL_GRAD_ALL"]+1),
                     ENROLL_UGRAD_DS     = np.log(df_ipeds["ENROLL_UGRAD_DS"]+1),
                     ENROLL_UGRAD_NDS    = np.log(df_ipeds["ENROLL_UGRAD_NDS"]+1),
                     INSTRUCT_EXP_PER_UG = np.log(df_ipeds["INSTRUCT_EXP_PER_UG"]+1),
                     RESEARCH_EXP_PER_UG = np.log(df_ipeds["RESEARCH_EXP_PER_UG"]+1),
                     ENDOWMENT_PER_UG    = np.log(df_ipeds["ENDOWMENT_PER_UG"]+1))
)

## scaling/normalizing data
scale     = StandardScaler()
df_scaled = scale.fit_transform(df_scaled.iloc[:,4:24]) 
df_scaled = pd.concat([df_ipeds.iloc[:,0:4], pd.DataFrame(df_scaled)], axis = 1)
df_scaled.columns = df_ipeds.columns

Below are the pairwise plots for the variables in our dataset. As expected, some variables are correlated. In some cases, the correlation reflects an inherent relationship (e.g. 4-year and 6-year graduation rates). In others, the association is less causal (e.g. 6-year graduation rate and the percentage of students receiving a Pell Grant).

In [3]:
## plotting pairwise comparisons
sns.pairplot(df_scaled.iloc[:,4:24])
Out[3]:
<seaborn.axisgrid.PairGrid at 0x2079ebf4ce0>
No description has been provided for this image

Next, we’ll use Principal Components Analysis (PCA) to reduce the number of features in our dataset. This offers two key benefits: first, it addresses multicollinearity among variables; second, it mitigates potential issues related to the “curse of dimensionality.”

As shown below, we’re able to reduce the number of features from 20 to 14 while retaining 95% of the variation in the data.

In [4]:
## PCA 
pca    = PCA(n_components = 0.95)
df_pca = pca.fit_transform(df_scaled.iloc[:,4:24])
df_pca = pd.DataFrame(df_pca, columns = [f"PC_{i+1}" for i in range(0, len(df_pca[0]))])

A quick look at the pairwise plots for our principal components confirms they are not correlated.

In [5]:
## plotting pairwise comparisons
sns.pairplot(df_pca.iloc[:,4:24])
Out[5]:
<seaborn.axisgrid.PairGrid at 0x207b41c3350>
No description has been provided for this image

Finally, we calculate the Euclidean distance between each school based on the 14 features. This distance serves as the foundation for identifying peer institutions—the underlying idea being that similar schools should be closer in feature space.

In [6]:
## Distance matrix
df_dist = pd.DataFrame(pairwise_distances(df_pca, metric = 'euclidean'), columns = df_ipeds["INST_ID"])
df_dist = pd.concat([df_ipeds.iloc[:,0:2], df_dist], axis = 1)

## transforming & cleaning
df_dist = (df_dist
           .melt(id_vars = ["INST_ID", "INST_NAME"], var_name   = "PEER_ID", value_name = "DISTANCE")
           .merge(df_ipeds.iloc[:,0:2], left_on = "PEER_ID", right_on = "INST_ID", how = "left")
           [["INST_ID_x", "INST_NAME_x", "INST_ID_y", "INST_NAME_y", "DISTANCE"]]
           .rename(columns = {"INST_ID_x"   : "INST_ID",
                              "INST_NAME_x" : "INST_NAME",
                              "INST_ID_y"   : "PEER_ID",
                              "INST_NAME_y" : "PEER_NAME"})
           .assign(DISTANCE = lambda x : round(x["DISTANCE"], 3))
)

Results¶

Below we can see the most similar schools to University of Utah - which include several other large, access-oriented flagship universities.

In [7]:
df_peers = (df_dist
            .loc[(df_dist["INST_ID"] == 230764)]
            .sort_values("DISTANCE")
            .head(11)
            .reset_index(drop = True)
)

df_peers[["PEER_NAME", "DISTANCE"]]
Out[7]:
PEER_NAME DISTANCE
0 University of Utah 0.000
1 University of Kansas 2.201
2 University of Nevada-Reno 2.248
3 Utah State University 2.322
4 University of Iowa 2.412
5 Kansas State University 2.543
6 University of Kentucky 2.567
7 The University of Montana 2.609
8 University of Toledo 2.683
9 Iowa State University 2.751
10 Louisiana State University and Agricultural & ... 2.760

We can plot the distribution of each variable for the peer institutions compared to all other institutions in our data set. The peers are characterized as having a slightly high admit rate, a higher graduation and retention rate, a greater proportion of non-resident students, larger endowments, and more money spent on research.

In [8]:
## 
df_temp = (df_ipeds
           .loc[df_ipeds["INST_ID"] != 230764]
           .assign(ENROLL_GRAD_ALL     = np.log(df_ipeds["ENROLL_GRAD_ALL"]+1),
                   ENROLL_UGRAD_DS     = np.log(df_ipeds["ENROLL_UGRAD_DS"]+1),
                   ENROLL_UGRAD_NDS    = np.log(df_ipeds["ENROLL_UGRAD_NDS"]+1),
                   INSTRUCT_EXP_PER_UG = np.log(df_ipeds["INSTRUCT_EXP_PER_UG"]+1),
                   RESEARCH_EXP_PER_UG = np.log(df_ipeds["RESEARCH_EXP_PER_UG"]+1),
                   ENDOWMENT_PER_UG    = np.log(df_ipeds["ENDOWMENT_PER_UG"]+1))
           .melt(id_vars = df_ipeds.iloc[:,0:4].columns, var_name = "VARIABLE", value_name = "VALUE")
           .merge(df_peers[["PEER_ID", "DISTANCE"]], left_on = "INST_ID", right_on = "PEER_ID", how = "left")
           .assign(PEER = lambda x : np.where(x["PEER_ID"].isnull(), "All Others", "Peers"))
)

## plotting variables
sns.catplot(data = df_temp, 
            kind = "violin", 
            hue  = "PEER",
            y    = "VALUE", 
            col  = "VARIABLE", 
            col_wrap = 5,
            sharey   = False)
Out[8]:
<seaborn.axisgrid.FacetGrid at 0x207be8a6630>
No description has been provided for this image

We can also examine the most similar schools to the University of California - Berkeley. This list contains several other UC schools as well as some more prestigious public univeristy from out east, such as UNC - Chapel Hill.

In [9]:
df_peers = (df_dist
            .loc[(df_dist["INST_ID"] == 110635)]
            .sort_values("DISTANCE")
            .head(11)
            .reset_index(drop = True)
)

df_peers[["PEER_NAME", "DISTANCE"]]
Out[9]:
PEER_NAME DISTANCE
0 University of California-Berkeley 0.000
1 University of California-Los Angeles 2.122
2 University of California-San Diego 2.789
3 University of California-Irvine 2.829
4 University of North Carolina at Chapel Hill 3.094
5 The University of Texas at Austin 3.129
6 University of California-Davis 3.396
7 University of Georgia 3.694
8 University of Michigan-Ann Arbor 3.841
9 Virginia Polytechnic Institute and State Unive... 3.847
10 University of Maryland-College Park 3.884

As you might expect, these schools have a much lower admit rate, incredibly high graduation and retention rates, and a much lower percent of students receiving a Pell Grant.

In [10]:
df_temp = (df_ipeds
           .loc[df_ipeds["INST_ID"] != 110635]
           .assign(ENROLL_GRAD_ALL     = np.log(df_ipeds["ENROLL_GRAD_ALL"]+1),
                   ENROLL_UGRAD_DS     = np.log(df_ipeds["ENROLL_UGRAD_DS"]+1),
                   ENROLL_UGRAD_NDS    = np.log(df_ipeds["ENROLL_UGRAD_NDS"]+1),
                   INSTRUCT_EXP_PER_UG = np.log(df_ipeds["INSTRUCT_EXP_PER_UG"]+1),
                   RESEARCH_EXP_PER_UG = np.log(df_ipeds["RESEARCH_EXP_PER_UG"]+1),
                   ENDOWMENT_PER_UG    = np.log(df_ipeds["ENDOWMENT_PER_UG"]+1))
           .melt(id_vars = df_ipeds.iloc[:,0:4].columns, var_name = "VARIABLE", value_name = "VALUE")
           .merge(df_peers[["PEER_ID", "DISTANCE"]], left_on = "INST_ID", right_on = "PEER_ID", how = "left")
           .assign(PEER = lambda x : np.where(x["PEER_ID"].isnull(), "All Others", "Peers"))
)

## plotting variables
sns.catplot(data = df_temp, 
            kind = "violin", 
            hue  = "PEER",
            y    = "VALUE", 
            col  = "VARIABLE", 
            col_wrap = 5,
            sharey   = False)
Out[10]:
<seaborn.axisgrid.FacetGrid at 0x207be2190d0>
No description has been provided for this image

And finally, the most similar schools to Missouri Western State University - a smaller, regional state school. Its list of peers contains several other regional universities.

In [11]:
df_peers = (df_dist
            .loc[(df_dist["INST_ID"] == 178387)]
            .sort_values("DISTANCE")
            .head(11)
            .reset_index(drop = True)
)

df_peers[["PEER_NAME", "DISTANCE"]]
Out[11]:
PEER_NAME DISTANCE
0 Missouri Western State University 0.000
1 The University of Texas Permian Basin 2.138
2 Southwestern Oklahoma State University 2.349
3 East Central University 2.444
4 Southeastern Oklahoma State University 2.580
5 Colorado State University Pueblo 2.669
6 Rogers State University 2.740
7 Southeastern Louisiana University 2.769
8 McNeese State University 2.838
9 Northeastern State University 2.861
10 University of Central Oklahoma 2.890

These schools have relatively less non-resident students, lower graduation and retention rates, a lower percentage of students living on campus (i.e. commuter schools), and a greater proportion of students receiving a Pell Grant.

In [12]:
df_temp = (df_ipeds
           .loc[df_ipeds["INST_ID"] != 178387]
           .assign(ENROLL_GRAD_ALL     = np.log(df_ipeds["ENROLL_GRAD_ALL"]+1),
                   ENROLL_UGRAD_DS     = np.log(df_ipeds["ENROLL_UGRAD_DS"]+1),
                   ENROLL_UGRAD_NDS    = np.log(df_ipeds["ENROLL_UGRAD_NDS"]+1),
                   INSTRUCT_EXP_PER_UG = np.log(df_ipeds["INSTRUCT_EXP_PER_UG"]+1),
                   RESEARCH_EXP_PER_UG = np.log(df_ipeds["RESEARCH_EXP_PER_UG"]+1),
                   ENDOWMENT_PER_UG    = np.log(df_ipeds["ENDOWMENT_PER_UG"]+1))
           .melt(id_vars = df_ipeds.iloc[:,0:4].columns, var_name = "VARIABLE", value_name = "VALUE")
           .merge(df_peers[["PEER_ID", "DISTANCE"]], left_on = "INST_ID", right_on = "PEER_ID", how = "left")
           .assign(PEER = lambda x : np.where(x["PEER_ID"].isnull(), "All Others", "Peers"))
)

## plotting variables
sns.catplot(data = df_temp, 
            kind = "violin", 
            hue  = "PEER",
            y    = "VALUE", 
            col  = "VARIABLE", 
            col_wrap = 5,
            sharey   = False)
Out[12]:
<seaborn.axisgrid.FacetGrid at 0x207c9d1a4b0>
No description has been provided for this image

Conclusion & Next Steps¶

This analysis is intended as a proof of concept rather than a definitive guide to identifying peer institutions. Ultimately, each school should determine which variables it wants to prioritize when selecting peers. Additionally, if schools wanted certain variables to have a greater impact when identifying peer institutes, this framework could be extended to weight certain variables more heavily. To do this, you would simply multiply a variable by a constant after standardizing features.